On the Path Integral in Imaginary Lobachevsky Space

The path integral on the single-sheeted hyperboloid, i.e.\ in $D$-dimensional imaginary Lobachevsky space, is evaluated. A potential problem which we call ``Kepler-problem'', and the case of a constant magnetic field are also discussed.Comment: 16 pages, LATEX, DESY 93-14

Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV

This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces \DIII and \DIV five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively

Long-distance remote comparison of ultrastable optical frequencies with 1e-15 instability in fractions of a second

We demonstrate a fully optical, long-distance remote comparison of independent ultrastable optical frequencies reaching a short term stability that is superior to any reported remote comparison of optical frequencies. We use two ultrastable lasers, which are separated by a geographical distance of more than 50 km, and compare them via a 73 km long phase-stabilized fiber in a commercial telecommunication network. The remote characterization spans more than one optical octave and reaches a fractional frequency instability between the independent ultrastable laser systems of 3e-15 in 0.1 s. The achieved performance at 100 ms represents an improvement by one order of magnitude to any previously reported remote comparison of optical frequencies and enables future remote dissemination of the stability of 100 mHz linewidth lasers within seconds.Comment: 7 pages, 4 figure

Zero-energy states for a class of quasi-exactly solvable rational potentials

Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schro\" odinger equation are constructed by starting from exactly solvable potentials for which the Schr\" odinger equation admits an so(2,1) potential algebra. For some of them, the zero-energy wave function is shown to be normalizable and to describe a bound state.Comment: LaTeX, 13 pages, 2 figures on request, to appear in Phys. Lett.

Signatures of pressure induced superconductivity in insulating Bi2212

We have performed several high pressure electrical resistance experiments on Bi1.98Sr2.06Y0.68Cu2O8, an insulating parent compound of the high-Tc Bi2212 family of copper oxide superconductors. We find a resistive anomaly, a downturn at low temperature, that onsets with applied pressure in the 20-40 kbar range. Through both resistance and magnetoresistance measurements, we identify this anomaly as a signature of induced superconductivity. Resistance to higher pressures decreases Tc, giving a maximum of 10 K. The higher pressure measurements exhibit a strong sensitivity to the hydrostaticity of the pressure environment. We make comparisons to the pressure induced superconductivity now ubiquitous in the iron arsenides.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional δ′\delta^{'}-function potential case

One-dimensional $\delta^{'}$-function potential is discussed in the framework of Green's function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green's function for this case is crucially dependent on the boundary conditions which are provided by self-adjoint extension method. The most general Green's function which contains four real self-adjoint extension parameters is constructed. Also the relation between the bare coupling constant and self-adjoint extension parameter is derived.Comment: LATEX, 13 page

Superconductivity on the threshold of magnetism in CePd2Si2 and CeIn3

The magnetic ordering temperature of some rare earth based heavy fermion compounds is strongly pressure-dependent and can be completely suppressed at a critical pressure, p$_c$, making way for novel correlated electron states close to this quantum critical point. We have studied the clean heavy fermion antiferromagnets CePd$_2$Si$_2$ and CeIn$_3$ in a series of resistivity measurements at high pressures up to 3.2 GPa and down to temperatures in the mK region. In both materials, superconductivity appears in a small window of a few tenths of a GPa on either side of p$_c$. We present detailed measurements of the superconducting and magnetic temperature-pressure phase diagram, which indicate that superconductivity in these materials is enhanced, rather than suppressed, by the closeness to magnetic order.Comment: 11 pages, including 9 figure

New Superconducting and Magnetic Phases Emerge on the Verge of Antiferromagnetism in CeIn3_3

We report the discovery of new superconducting and novel magnetic phases in CeIn$_3$ on the verge of antiferromagnetism (AFM) under pressure ($P$) through the In-nuclear quadrupole resonance (NQR) measurements. We have found a $P$-induced phase separation of AFM and paramagnetism (PM) without any trace for a quantum phase transition in CeIn$_3$. A new type of superconductivity (SC) was found in $P=2.28-2.5$ GPa to coexist with AFM that is magnetically separated from PM where the heavy fermion SC takes place. We propose that the magnetic excitations such as spin-density fluctuations induced by the first-order magnetic phase transition might mediate attractive interaction to form Cooper pairs.Comment: 4 pages, 4 EPS figures, submitted to J. Phys. Soc. Jp